code: def test_exp_and_dist_and_projection_to_tangent_space(
      self, vector, base_point
  ):
      tangent_vec = self.space.to_tangent(
          vector=vector, base_point=base_point
      )
      exp = self.space.metric.exp(
          tangent_vec=tangent_vec, base_point=base_point
      )
      result = self.space.metric.dist(base_point, exp)
      expected = gs.linalg.norm(tangent_vec) % (2 * gs.pi)
      self.assertAllClose(result, expected)
  
imports: import random
  import pytest
  import geomstats.backend
  from geomstats.geometry.hypersphere import Hypersphere, HypersphereMetric
  from geomstats.test.parametrizers import DataBasedParametrizer
  from geomstats.test.random import HypersphereIntrinsicRandomDataGenerator
  from geomstats.test_cases.geometry.hypersphere import HypersphereCoordsTransformTestCase, HypersphereExtrinsicTestCase, HypersphereIntrinsicTestCase
  from geomstats.test_cases.geometry.riemannian_metric import RiemannianMetricTestCase
  from .data.hypersphere import Hypersphere2ExtrinsicMetricTestData, Hypersphere2IntrinsicMetricTestData, Hypersphere4ExtrinsicMetricTestData, HypersphereCoordsTransformTestData, HypersphereExtrinsicMetricTestData, HypersphereExtrinsicTestData, HypersphereIntrinsicTestData
label_desc: Use image node_id 1 for calling the TestHypersphere4ExtrinsicMetric obj's underlying member method code with example usage: obj.test_exp_and_dist_and_projection_to_tangent_space(vector, base_point) without return types